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BEGIN:VEVENT
SUMMARY:Michael Entov (Technion)
DTSTART:20200422T111000Z
DTEND:20200422T123000Z
DTSTAMP:20260404T094529Z
UID:GDS/1
DESCRIPTION:Title: Rigidity of Lagrangian tori in K3 surfaces\nby Michael Entov (Techn
ion) as part of Geometry and Dynamics seminar\n\n\nAbstract\nA Kahler-type
form is a symplectic form compatible with an integrable \ncomplex structu
re. Sheridan and Smith previously proved\, using deep \nmethods of homolog
ical mirror symmetry\, that for any Maslov-zero \nLagrangian torus L in a
K3 surface M equipped with a Kahler-type \nform of a *particular kind*\, t
he integral homology class of L has \nto be non-zero and primitive. I will
discuss how to extend this \nresult to *arbitrary* Kahler-type forms on M
using dynamical \nproperties of the action of the diffeomorphism group of
M on the \nspace of such forms. These dynamical properties are obtained u
sing \na version of Ratner's theorem. This is a joint work in progress \nw
ith M.Verbitsky.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Boris Vertman (University of Oldenburg)
DTSTART:20200506T111000Z
DTEND:20200506T123000Z
DTSTAMP:20260404T094529Z
UID:GDS/2
DESCRIPTION:Title: Mean curvature flow in Lorentzian space times\nby Boris Vertman (Un
iversity of Oldenburg) as part of Geometry and Dynamics seminar\n\n\nAbstr
act\nHypersurfaces of zero or constant mean curvature play a central \nrol
e in the proof of the Positive Mass Theorem and also in the \nanalysis of
the Cauchy problem for asymptotically flat space-times. \nMean curvature f
low can be a tool to construct such hypersurfaces. \nWe discuss local exis
tence of the flow for non-compact space-like \nhypersurfaces in Robertson-
Walker space-times. This is a joint project \nwith Giuseppe Gentile.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louis Ioos (Tel Aviv University)
DTSTART:20200513T111000Z
DTEND:20200513T123000Z
DTSTAMP:20260404T094529Z
UID:GDS/3
DESCRIPTION:Title: Almost-representations of the Lie algebra of SU(2) and quantization of
the sphere\nby Louis Ioos (Tel Aviv University) as part of Geometry an
d Dynamics seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/GDS/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tsachik Gelander (Weizmann Institute of Science)
DTSTART:20200520T111000Z
DTEND:20200520T123000Z
DTSTAMP:20260404T094529Z
UID:GDS/4
DESCRIPTION:Title: Convergence of normalized Betti numbers in nonpositive curvature\nb
y Tsachik Gelander (Weizmann Institute of Science) as part of Geometry and
Dynamics seminar\n\n\nAbstract\nI will show that if X is any symmetric sp
ace other than 3-dimensional \nhyperbolic space and M is any finite volume
manifold that is a quotient \nof X\, then the normalized Betti numbers of
M are "testable"\, i.e. one \ncan guess their values by sampling the mani
fold at random places. This \nis joint with Abert\, Biringer and Bergeron\
, and extends some of our \nolder work with Nikolov\, Raimbault and Samet.
The content of the recent \npaper involves a random discretization proces
s that converts the "thick \npart" of M into a simplicial complex\, togeth
er with analysis of the \n"thin parts" of M. As a corollary\, we obtain th
at whenever X is a higher \nrank irreducible symmetric space and M_i is an
y sequence of distinct \nfinite volume quotients of X\, the normalized Bet
ti numbers of the M_i \nconverge to the "L^2-Betti numbers" of X.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victor Ivrii (University of Toronto)
DTSTART:20200527T111000Z
DTEND:20200527T123000Z
DTSTAMP:20260404T094529Z
UID:GDS/5
DESCRIPTION:Title: Heavy atoms and molecules: Thomas-Fermi and Scott approximations\nb
y Victor Ivrii (University of Toronto) as part of Geometry and Dynamics se
minar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/GDS/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Mazzucchelli (ENS de Lyon)
DTSTART:20200603T111000Z
DTEND:20200603T123000Z
DTSTAMP:20260404T094529Z
UID:GDS/6
DESCRIPTION:Title: Closed geodesics on reversible Finsler 2-spheres\nby Marco Mazzucch
elli (ENS de Lyon) as part of Geometry and Dynamics seminar\n\n\nAbstract\
nIn this talk\, I will show that two celebrated theorems on closed \ngeode
sics of Riemannian 2-spheres still hold for the larger class \nof reversib
le Finsler 2-spheres: Lusternik-Schnirelmann's theorem \nasserting the exi
stence of three simple closed geodesics\, and \nBangert-Franks-Hingston's
theorem asserting the existence of \ninfinitely many closed geodesics. I w
ill sketch the proofs of \nthese statements\, employing in particular the
Finsler generalization \nof Grayson's curve shortening flow developed by A
ngenent-Oaks. \nThis is joint work with Guido De Philippis\, Michele Marin
i\, and \nStefan Suhr.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ran Tessler (Weizmann Institute of Science)
DTSTART:20200617T111000Z
DTEND:20200617T123000Z
DTSTAMP:20260404T094529Z
UID:GDS/8
DESCRIPTION:Title: Open r-spin intersection theory\nby Ran Tessler (Weizmann Institute
of Science) as part of Geometry and Dynamics seminar\n\n\nAbstract\nIn 19
92 Witten conjectured that the intersection theory on the moduli \nof r-sp
in curves gives rise to a Gelfand Dickey tau function\, and \nproved his c
onjecture in genus 0.\nRecently\, in a joint work with Buryak and Clader w
e made a similar \nconjecture/construction in the open setting:\nWe conjec
tured that intersection theory on the moduli of r-spin \nsurfaces with bou
ndaries should give rise to the Gelfand Dickey *wave* \nfunction and prove
d it in genus 0. In my talk I will describe all this\, \nin particular\, I
'll explain what is an r-spin structure\, what is the \nGelfand-Dickey hie
rarchy and what is the motivation. If time permits\, \na mirror theorem (b
ased on work with Gross and Kelly) will also be shown.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emanuel Milman (Technion)
DTSTART:20200622T111000Z
DTEND:20200622T123000Z
DTSTAMP:20260404T094529Z
UID:GDS/9
DESCRIPTION:Title: Functional Inequalities on sub-Riemannian manifolds via QCD\nby Ema
nuel Milman (Technion) as part of Geometry and Dynamics seminar\n\n\nAbstr
act\nWe are interested in obtaining Poincare and log-Sobolev inequalities
\non domains in sub-Riemannian manifolds (equipped with their natural \nsu
b-Riemannian metric and volume measure).\n\nIt is well-known that strictly
sub-Riemannian manifolds do not satisfy \nany type of Curvature-Dimension
condition CD(K\,N)\, introduced by \nLott-Sturm-Villani some 15 years ago
\, so we must follow a different \npath. We show that while ideal (strictl
y) sub-Riemannian manifolds do \nnot satisfy any type of CD condition\, th
ey do satisfy a quasi-convex \nrelaxation thereof\, which we name QCD(Q\,K
\,N). As a consequence\, these \nspaces satisfy numerous functional inequa
lities with exactly the same \nquantitative dependence (up to a factor of
Q) as their CD counterparts. \nWe achieve this by extending the localizati
on paradigm to completely \ngeneral interpolation inequalities\, and a one
-dimensional comparison \nof QCD densities with their "CD upper envelope".
We thus obtain the \nbest known quantitative estimates for (say) the L^p
-Poincare and \nlog-Sobolev inequalities on domains in the ideal sub-Riema
nnian setting\, \nwhich in particular are independent of the topological d
imension. For \ninstance\, the classical Li-Yau / Zhong-Yang spectral-gap
estimate holds \non all Heisenberg groups of arbitrary dimension up to a f
actor of 4.\n\nNo prior knowledge will be assumed\, and we will (hopefully
) explain \nall of the above notions during the talk.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Uri Bader (Weizmann Institute of Science)
DTSTART:20200624T111000Z
DTEND:20200624T123000Z
DTSTAMP:20260404T094529Z
UID:GDS/10
DESCRIPTION:Title: Totally geodesic subspaces and arithemeticity phenomena in hyperbolic
manifolds\nby Uri Bader (Weizmann Institute of Science) as part of Geo
metry and Dynamics seminar\n\n\nAbstract\nIn this talk I will survey a wel
l known\, still wonderful\, connection \nbetween geometry and arithmetics
and discuss old and new results in \nthis topic. The starting point of the
story is Cartan's discovery \nof the correspondence between semisimple Li
e groups and symmetric \nspaces. Borel and Harish-Chandra\, following Sieg
el\, later realized \na fantastic further relation between arithmetic subg
roups of semisimple \nLie groups and locally symmetric space - every arith
emtic group gives \na locally symmetric space of finite volume. The best k
nown example \nis the modular curve which is associated in this way with t
he group \nSL_2(Z). This relation has a partial converse\, going under the
name \n"arithmeticity theorem"\, which was proven\, under a higher rank \
nassumption\, by Margulis and in some rank one situations by Corlette \nan
d Gromov-Schoen. The rank one setting is related to hyperbolic \ngeometry
- real\, complex\, quaternionic or octanionic.\nThere are several open que
stions regarding arithmeticity of locally \nhyperbolic manifolds of finite
volume over the real or complex fields \nand there are empirical evidence
s relating these questions to the \ngeometry of totally geodesic submanifo
lds. \nRecently\, some of these questions were solved by Margulis-Mohammad
i \n(real hyp. 3-dim)\, Baldi-Ullmo (complex hyp.) and B-Fisher-Miller-Sto
ver. \nThe techniques involve a mixture of ergodic theory\, algebraic grou
ps \ntheory and hodge theory. After surveying the above story\, explaining
\nall the terms and discussing some open questions\, I hope to have a \nl
ittle time to say something about the proofs.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yusuke Kawamoto (Ecole Normale Superieure)
DTSTART:20200701T111000Z
DTEND:20200701T123000Z
DTSTAMP:20260404T094529Z
UID:GDS/11
DESCRIPTION:Title: Homogeneous quasimorphism\, C^0-topology and Lagrangian intersection\nby Yusuke Kawamoto (Ecole Normale Superieure) as part of Geometry and
Dynamics seminar\n\n\nAbstract\nThe goal of the talk is to construct a non
-trivial homogeneous \nquasimorphism on the group of Hamiltonian diffeomor
phisms of the \n2- and 4-dimensional quadric which is continuous with resp
ect to both \nC^0-topology and the Hofer metric. This answers a variant of
a question \nof Entov-Polterovich-Py. A comparison of spectral invariants
for \nquantum cohomology rings with different coefficient fields plays a
\ncrucial role in the proof which might be of independent interest. \nIf t
ime permits\, we will see how this comparison can be used to answer \na qu
estion of Polterovich-Wu.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew Lobb (Durham University)
DTSTART:20201028T121000Z
DTEND:20201028T133000Z
DTSTAMP:20260404T094529Z
UID:GDS/12
DESCRIPTION:Title: The rectangular peg problem\nby Andrew Lobb (Durham University) as
part of Geometry and Dynamics seminar\n\n\nAbstract\nFor any smooth Jorda
n curve and rectangle in the plane\, we show that \nthere exist four point
s on the Jordan curve forming the vertices of a \nrectangle similar to the
given one. Joint work with Josh Greene.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laszlo Lempert (Purdue University)
DTSTART:20201104T151000Z
DTEND:20201104T163000Z
DTSTAMP:20260404T094529Z
UID:GDS/13
DESCRIPTION:Title: On the adjoint action of symplectomorphism groups\nby Laszlo Lempe
rt (Purdue University) as part of Geometry and Dynamics seminar\n\n\nAbstr
act\nMotivated by constructions in Kähler geometry\, in this talk we cons
ider \na compact symplectic manifold $(X\,\\omega)$ and the group $G$ of i
ts \nsymplectomorphisms. We study the action of $G$ on the Fréchet space
\n$C^\\infty(X)$ of smooth functions\, by pullback\, and describe properti
es of \nconvex functions $p:C^\\infty(X)\\to\\mathbb R$ that are invariant
under this \naction.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bo Berndtsson (Chalmers University of Technology)
DTSTART:20201111T121000Z
DTEND:20201111T133000Z
DTSTAMP:20260404T094529Z
UID:GDS/14
DESCRIPTION:Title: Complex integrals and Kuperberg's proof of the Bourgain-Milman theorem
\nby Bo Berndtsson (Chalmers University of Technology) as part of Geom
etry and Dynamics seminar\n\n\nAbstract\nI will show a function version of
the Bourgain-Milman theorem:\n$$ \\int e^{-\\phi}\\int e^{-\\phi^*}\\geq
\\pi^n $$\,\nif $\\phi$ is a symmetric convex function on $\\R^n$ and $\\
phi^*$ is its \nLegendre transform. The proof is inspired by Kuperberg's p
roof of the \nBourgain-Milman theorem but uses complex analytic techniques
.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Misha Bialy (Tel Aviv University)
DTSTART:20201118T121000Z
DTEND:20201118T133000Z
DTSTAMP:20260404T094529Z
UID:GDS/15
DESCRIPTION:Title: The Birkhoff-Poritsky conjecture for centrally-symmetric billiard tabl
es\nby Misha Bialy (Tel Aviv University) as part of Geometry and Dynam
ics seminar\n\n\nAbstract\nIn this talk (joint work with A.E. Mironov) I s
hall discuss a recent \nproof of the Birkhoff-Poritsky conjecture for cent
rally-symmetric \nC^2-smooth convex planar billiards. We assume that the d
omain between \nthe invariant curve of 4-periodic orbits and the boundary
of the phase \ncylinder is foliated by C^0-invariant curves. Under this a
ssumption we \nprove that the billiard curve is an ellipse. The main ingre
dients of \nthe proof are : (1) the non-standard generating function for c
onvex \nbilliards\; (2) the remarkable structure of the invariant curve \n
consisting of 4-periodic orbits\; and (3) the integral-geometry \napproach
initiated for rigidity results of circular billiards. \nSurprisingly\, ou
r result yields a Hopf-type rigidity for billiard \nin ellipse.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vinicius G. B. Ramos (IMPA\, Brazil)
DTSTART:20201202T151000Z
DTEND:20201202T163000Z
DTSTAMP:20260404T094529Z
UID:GDS/16
DESCRIPTION:Title: Examples around the strong Viterbo conjecture\nby Vinicius G. B. R
amos (IMPA\, Brazil) as part of Geometry and Dynamics seminar\n\n\nAbstrac
t\nThe Viterbo conjecture states that the ball maximizes any normalized \n
symplectic capacity within all convex sets in R^{2n} of a fixed volume \na
nd that it is the unique maximizer. A stronger conjecture says that \nall
normalized capacities coincide for convex sets. In joint work with \nGutt
and Hutchings\, we prove the stronger conjecture for a somewhat \ndifferen
t class of 4-dimensional domains\, namely toric domains with a \ndynamical
ly convex toric boundary. In joint work with Ostrover and Sepe\, \nwe prov
e that a 4-dimensional Lagrangian product which is a maximizer \nof the Ho
fer-Zehnder capacity is non-trivially symplectomorphic to a \nball giving
further evidence to the uniqueness claim of Viterbo's \nconjecture. In thi
s talk\, I will explain the proof of these two results.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Frol Zapolsky (University of Haifa)
DTSTART:20201125T121000Z
DTEND:20201125T133000Z
DTSTAMP:20260404T094529Z
UID:GDS/17
DESCRIPTION:Title: Relative symplectic cohomology and ideal-valued measures\nby Frol
Zapolsky (University of Haifa) as part of Geometry and Dynamics seminar\n\
n\nAbstract\nIn a joint work in progress together with A. Dickstein\, Y. G
anor\, and \nL. Polterovich we prove new symplectic rigidity results. Firs
t\, we \ncategorify the notion of a heavy subset of a symplectic manifold
(due \nto Entov-Polterovich)\, and in particular provide a simple algebrai
c \ncriterion which guarantees that two heavy sets intersect. Next\, we \n
treat involutive maps defined on a symplectic manifold M\; a smooth \nmap
M -> B is involutive if pullbacks of smooth functions on B Poisson \ncommu
te. For such maps we prove a refinement of Entov-Polterovich's \nnondispla
ceable fiber theorem\, as well as a symplectic Tverberg-type \ntheorem\, w
hich roughly says that each involutive map into a manifold \nof sufficient
ly low dimension has a fiber which intersects a wide \nfamily of subsets o
f M.\n\nAll of these results are proved using a generalized version of Gro
mov's \nnotion of ideal-valued measures\, which furnish an easily digestib
le \nway to package the relevant information. We construct such measures \
nusing relative symplectic cohomology\, an invariant recently introduced \
nby U. Varolgunes\, who also proved the Mayer-Vietoris property for it\, \
non which our work relies in a crucial manner. Our main technical \ninnova
tion is the relative symplectic cohomology of a pair\, whose \nconstructio
n is inspired by homotopy theory.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lev Birbrair (Universidade Federal do Ceará\, Brazil)
DTSTART:20201209T121000Z
DTEND:20201209T133000Z
DTSTAMP:20260404T094529Z
UID:GDS/18
DESCRIPTION:Title: Lipschitz geometry of surface germs in $\\R^4$: metric knots\nby L
ev Birbrair (Universidade Federal do Ceará\, Brazil) as part of Geometry
and Dynamics seminar\n\n\nAbstract\nA link at the origin of an isolated si
ngularity of a two-dimensional \nsemialgebraic surface in $\\R^4$ is a top
ological knot (or link) in $S^3$. \nWe study the connection between the am
bient Lipschitz geometry of \nsemialgebraic surface germs in $\\R^4$ and t
he knot theory. Namely\, for \nany knot $K$\, we construct a surface $X_K$
in $\\R^4$ such that: $X_K$ \nhas a trivial knot at the origin\; the germ
s $X_K$ are outer bi-Lipschitz \nequivalent for all $K$\; two germs $X_{K}
$ and $X_{K'}$ are ambient \nbi-Lipschitz equivalent only if the knots $K$
and $K'$ are isotopic.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Barak Weiss (Tel Aviv University)
DTSTART:20201216T121000Z
DTEND:20201216T133000Z
DTSTAMP:20260404T094529Z
UID:GDS/19
DESCRIPTION:Title: Ergodicity of rel foliations on the space of holomorphic one forms
\nby Barak Weiss (Tel Aviv University) as part of Geometry and Dynamics se
minar\n\n\nAbstract\nThe rel foliation is a foliation of the moduli space
of abelian \ndifferentials obtained by "moving the zeroes of the one form
while \nkeeping all absolute periods fixed". It has been studied in comple
x \nanalysis and dynamics under different names (isoperiodic foliation\, \
nSchiffer variation\, kernel foliation). Until recent years the question \
nof its ergodicity was wide open. Recently partial results were obtained \
nby Calsamiglia-Deroin-Francaviglia and by Hamenstadt. In our work we \nco
mpletely resolve the ergodicity question. Joint work in progress with \nJo
n Chaika and Alex Eskin\, based on a far-reaching extension of a \ncelebra
ted result of Eskin and Mirzakhani. All relevant notions will \nbe explai
ned in the lecture and no prior familiarity with dynamics on \nspaces of o
ne forms will be assumed.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ood Shabtai (Tel Aviv University)
DTSTART:20201223T121000Z
DTEND:20201223T133000Z
DTSTAMP:20260404T094529Z
UID:GDS/20
DESCRIPTION:Title: On polynomials in two spectral projections of spin operators\nby O
od Shabtai (Tel Aviv University) as part of Geometry and Dynamics seminar\
n\n\nAbstract\nWe discuss the semiclassical behavior of an arbitrary bivar
iate \npolynomial evaluated on a pair of spectral projections of spin \nop
erators\, and compare it with its value on a pair of random \nprojections.
\n
LOCATION:https://stable.researchseminars.org/talk/GDS/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shira Tanny (Tel Aviv University)
DTSTART:20201230T121000Z
DTEND:20201230T133000Z
DTSTAMP:20260404T094529Z
UID:GDS/21
DESCRIPTION:Title: A max-inequality for spectral invariants of disjointly supported Hamil
tonians\nby Shira Tanny (Tel Aviv University) as part of Geometry and
Dynamics seminar\n\n\nAbstract\nThe relation between spectral invariants o
f disjointly supported \nHamiltonians and that of their sum was studied by
Humiliere\, Le Roux \nand Seyfaddini on aspherical manifolds. We study th
is relation in a \nwider setting and derive applications to Polterovich's
Poisson bracket \ninvariant. This is a work in progress.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vincent Humilière (Sorbonne University)
DTSTART:20210106T121000Z
DTEND:20210106T133000Z
DTSTAMP:20260404T094529Z
UID:GDS/22
DESCRIPTION:Title: Is the group of compactly supported area preserving homeomorphisms of
the 2-disk simple?\nby Vincent Humilière (Sorbonne University) as par
t of Geometry and Dynamics seminar\n\n\nAbstract\nThis long standing open
problem has been recently solved in joint work \nwith Dan Cristofaro-Gardi
ner and Sobhan Seyfaddini. I will present some \nbackground and the main i
deas that lead to the proof. It is based on \ntools from symplectic topolo
gy and more precisely on a theory due to \nHutchings\, called Periodic Flo
er Homology.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dan Mangoubi (The Hebrew University of Jerusalem)
DTSTART:20210113T121000Z
DTEND:20210113T133000Z
DTSTAMP:20260404T094529Z
UID:GDS/23
DESCRIPTION:Title: A Local version of Courant's Nodal domain Theorem\nby Dan Mangoubi
(The Hebrew University of Jerusalem) as part of Geometry and Dynamics sem
inar\n\n\nAbstract\nLet u_k be an eigenfunction of a vibrating string (wit
h fixed ends) \ncorresponding to the k-th eigenvalue. It is not difficult
to show that \nthe number of zeros of u_k is exactly k+1. Equivalently\, t
he number of \nconnected components of the complement of $u_k=0$ is $k$.\n
\nIn 1923 Courant found that in higher dimensions (considering eigenfuncti
ons \nof the Laplacian on a closed Riemannian manifold M) the number of co
nnected \ncomponents of the open set $M\\setminus {u_k=0}$ is at most $k$.
\n\nIn 1988 Donnelly and Fefferman gave a bound on the number of connected
\ncomponents of $B\\setminus {u_k=0}$\, where $B$ is a ball in $M$. Howev
er\, \ntheir estimate was not sharp (even for spherical harmonics).\n\nWe
describe the ideas which give the sharp bound on the number of connected \
ncomponents in a ball. The talk is based on a joint work with S. Chanillo\
, \nA. Logunov and E. Malinnikova\, with a contribution due to F. Nazarov.
\n
LOCATION:https://stable.researchseminars.org/talk/GDS/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Boaz Klartag (Weizmann Institute of Science)
DTSTART:20210303T121000Z
DTEND:20210303T133000Z
DTSTAMP:20260404T094529Z
UID:GDS/24
DESCRIPTION:Title: Rigidity of Riemannian embeddings of discrete metric spaces\nby Bo
az Klartag (Weizmann Institute of Science) as part of Geometry and Dynamic
s seminar\n\n\nAbstract\nLet M be a complete\, connected Riemannian surfac
e and\nsuppose that S is a discrete subset of M. What can we learn about M
\nfrom the knowledge of all distances in the surface between pairs of\npoi
nts of S? We prove that if the distances in S correspond to the\ndistances
in a 2-dimensional lattice\, or more generally in an\narbitrary net in R^
2\, then M is isometric to the Euclidean plane. We\nthus find that Riemann
ian embeddings of certain discrete metric spaces\nare rather rigid. A coro
llary is that a subset of Z^3 that strictly\ncontains a two-dimensional la
ttice cannot be isometrically embedded in\nany complete Riemannian surface
. This is a joint work with M. Eilat.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Cristofaro-Gardiner (IAS Princeton\; University of Californ
ia\, Santa Cruz)
DTSTART:20210310T121000Z
DTEND:20210310T133000Z
DTSTAMP:20260404T094529Z
UID:GDS/25
DESCRIPTION:Title: The subleading asymptotics of the ECH spectrum\nby Daniel Cristofa
ro-Gardiner (IAS Princeton\; University of California\, Santa Cruz) as par
t of Geometry and Dynamics seminar\n\n\nAbstract\nEmbedded contact homolog
y can be used to associate a sequence of spectral \ninvariants\, called EC
H spectral invariants\, to any closed three-manifold \nwith a contact form
. In previous joint work\, we proved a “Volume Property” \nthat recov
ers the volume of any such manifold from the asymptotics of its \nECH spec
tral invariants. I will discuss recent work aimed at better \nunderstandi
ng the subleading asymptotics of this sequence. The main \nsubject of my
talk will be a joint work with Nikhil Savale in which we \nprove a new bou
nd on the growth rate of the subleading asymptotics. \nI will also briefl
y mention a conjecture\, due to Hutchings\, concerning \nrecovering the
“contact Ruelle invariant” from the subleading asymptotics.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitry Faifman (Tel Aviv University)
DTSTART:20210317T121000Z
DTEND:20210317T133000Z
DTSTAMP:20260404T094529Z
UID:GDS/26
DESCRIPTION:Title: Around the Funk metric and its billiards\nby Dmitry Faifman (Tel A
viv University) as part of Geometry and Dynamics seminar\n\n\nAbstract\nTh
e Funk metric in the interior of a convex body is a lesser known \nrelativ
e of the projectively-invariant Hilbert metric\, yet in some \nways simple
r and more natural. Starting with a few simple observations\, \nwe will ex
plore some Funk-inspired generalizations of well-known \nresults in the ge
ometry of normed spaces and Minkowski billiards\, \nsuch as Sch\\"affer's
dual girth conjecture and the Gutkin-Tabachnikov \nduality. I will also of
fer a Funk approach to the integrability of the \nhyperbolic billiard in a
conic. Time permitting\, I will discuss the \nvolume of metric balls in F
unk geometry\, leading to a generalization \nof the Blaschke-Santalo inequ
ality.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Peralta-Salas (ICMAT Madrid)
DTSTART:20210324T121000Z
DTEND:20210324T133000Z
DTSTAMP:20260404T094529Z
UID:GDS/27
DESCRIPTION:Title: Turing completeness and universality of steady Euler flows\nby Dan
iel Peralta-Salas (ICMAT Madrid) as part of Geometry and Dynamics seminar\
n\n\nAbstract\nI will review recents results on the Turing completeness an
d universality \nof steady solutions to the Euler equations. In particular
\, I will show \nthe existence of three-dimensional fluid flows exhibiting
undecidable \ntrajectories and discuss other universality features such a
s embeddability \nof diffeomorphisms into steady Euler states. These resul
ts are motivated by \nTao's programme to address the blow-up problem for t
he Navier-Stokes \nequations based on the Turing completeness of the fluid
flows. This is \nbased on joint works with Robert Cardona\, Eva Miranda a
nd Francisco Presas.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Rosen (Ruhr-Universität Bochum)
DTSTART:20210407T111000Z
DTEND:20210407T123000Z
DTSTAMP:20260404T094529Z
UID:GDS/28
DESCRIPTION:Title: Random inscribed polytopes in Non-Euclidean Geometries\nby Daniel
Rosen (Ruhr-Universität Bochum) as part of Geometry and Dynamics seminar\
n\n\nAbstract\nRandom polytopes have a long history\, going back to Sylves
ter's famous \nfour-point problem. Since then their study has become a mai
nstream topic \nin convex and stochastic geometry\, with close connection
to polytopal \napproximation problems\, among other things. In this talk w
e will consider \nrandom polytopes in constant curvature geometries\, and
show that their \nvolume satisfies a central limit theorem. The proof uses
Stein's method \nfor normal approximation\, and extends to general projec
tive Finsler metrics.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Melistas (University of Georgia)
DTSTART:20210421T111000Z
DTEND:20210421T123000Z
DTSTAMP:20260404T094529Z
UID:GDS/29
DESCRIPTION:Title: The Large-Scale Geometry of Overtwisted Contact Forms\nby Thomas M
elistas (University of Georgia) as part of Geometry and Dynamics seminar\n
\n\nAbstract\nInspired by the symplectic Banach-Mazur distance\, proposed
by Ostrover\n and Polterovich in the setting of non-degenerate starshaped
domains of \nLiouville manifolds\, we define a distance on the space of co
ntact forms \nsupporting a given contact structure on a closed contact man
ifold. We \ncompare it to a recently defined contact Banach-Mazur distance
by Rosen \nand Zhang and we use it in order to bi-Lipschitz embed part of
the \n2-dimensional Euclidean space into the space of overtwisted contact
\nforms supporting a given contact structure on a smooth closed manifold.
\n
LOCATION:https://stable.researchseminars.org/talk/GDS/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zvi Shem-Tov (The Hebrew University of Jerusalem)
DTSTART:20210428T111000Z
DTEND:20210428T123000Z
DTSTAMP:20260404T094529Z
UID:GDS/30
DESCRIPTION:Title: Conjugation-invariant norms on arithmetic groups\nby Zvi Shem-Tov
(The Hebrew University of Jerusalem) as part of Geometry and Dynamics semi
nar\n\n\nAbstract\nA classical theorem of Ostrowski says that every absolu
te value on the \nfield of rational numbers\, or equivalently on the ring
of integers\, is \nequivalent to either the standard (real) absolute value
\, or a $p$-adic \nabsolute value\, for which the closure of the integers
is compact. In \nthis talk we will see a non-abelian analogue of this resu
lt for \n$SL(n\\ge3\,\\Z)$\, and related groups of arithmetic type. We wil
l see \na relation to the celebrated Margulis' normal subgroup theorem\, a
nd \nderive rigidity results for homomorphisms into certain non-locally \n
compact groups -- those endowed with a bi-invariant metric. We will \nalso
discuss a relation to the deep work of Nikolov-Segal on profinite \ngroup
s. This is a joint work with Leonid Polterovich and Yehuda Shalom.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Otto van Koert (Seoul National University)
DTSTART:20210505T111000Z
DTEND:20210505T123000Z
DTSTAMP:20260404T094529Z
UID:GDS/31
DESCRIPTION:Title: A generalization of the Poincare-Birkhoff fixed point theorem and the
restricted three-body problem\nby Otto van Koert (Seoul National Unive
rsity) as part of Geometry and Dynamics seminar\n\n\nAbstract\nIn joint wo
rk with Agustin Moreno\, we propose a generalization of the \nPoincare-Bir
khoff fixed point theorem. We start with a construction of \nglobal hypers
urfaces of section in the spatial three-body problem\, describe \nsome ret
urn maps and suggest some generalizations of the Poincare-Birkhoff \nfixed
point theorem. We use symplectic homology in the proof of our theorem.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Georgios Dimitroglou Rizell (Uppsala University)
DTSTART:20210512T111000Z
DTEND:20210512T123000Z
DTSTAMP:20260404T094529Z
UID:GDS/32
DESCRIPTION:Title: Non-degeneracy of Legendrians from bifurcation of contact homology
\nby Georgios Dimitroglou Rizell (Uppsala University) as part of Geometry
and Dynamics seminar\n\n\nAbstract\nWe show that the invariance of Legendr
ian contact homology can be \nformulated in terms of a bifurcation analysi
s whose action properties \nare continuous with respect to the oscillatory
norm of the contact \nHamiltonian. (I.e. the barcode varies continuously
with respect to \nthe same.) Combined with work of Rosen-Zhang this implie
s non-degeneracy \nof the Shelukhin-Chekanov-Hofer metric on the space of
Legendrian \nembeddings. We also explain how convex surface techniques in
dimension \nthree can be used to prove a statement related to the converse
: a \nnon-Legendrian knot cannot be approximated by the image of a Legendr
ian \nknot under a sequence of C0-converging contactomorphisms. This is jo
int \nwork with M. Sullivan.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luis Diogo (Fluminense Federal University)
DTSTART:20210519T111000Z
DTEND:20210519T123000Z
DTSTAMP:20260404T094529Z
UID:GDS/33
DESCRIPTION:Title: Monotone Lagrangians in cotangent bundles of spheres\nby Luis Diog
o (Fluminense Federal University) as part of Geometry and Dynamics seminar
\n\n\nAbstract\nAmong all Lagrangian submanifolds of a symplectic manifold
\, the class of \nmonotone Lagrangians is often very rich and nicely suite
d to being studied \nusing pseudoholomophic curves. We find a family of mo
notone Lagrangians \nin cotangent bundles of spheres with the following pr
operty: every compact \nmonotone Lagrangian with non-trivial Floer cohomol
ogy cannot be displaced \nby a Hamiltonian diffeomorphism from at least on
e element in the family. \nThis follows from the fact that the Lagrangians
in the family split-generate \nthe compact monotone Fukaya category. This
is joint work with Mohammed Abouzaid.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonathan David Evans (Lancaster University)
DTSTART:20210526T111000Z
DTEND:20210526T123000Z
DTSTAMP:20260404T094529Z
UID:GDS/34
DESCRIPTION:Title: A Lagrangian Klein bottle you can't squeeze\nby Jonathan David Eva
ns (Lancaster University) as part of Geometry and Dynamics seminar\n\n\nAb
stract\nGiven a nonorientable Lagrangian surface L in a symplectic 4-manif
old\, \nhow far can you deform the symplectic form before there is no Lagr
angian \nsurface isotopic to L? I will discuss this problem in general and
explain \nthe solution in a particular case.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeff Hicks (University of Cambridge)
DTSTART:20210602T111000Z
DTEND:20210602T123000Z
DTSTAMP:20260404T094529Z
UID:GDS/35
DESCRIPTION:Title: Decompositions of Lagrangian Cobordisms\nby Jeff Hicks (University
of Cambridge) as part of Geometry and Dynamics seminar\n\n\nAbstract\nCon
sider a symplectic manifold X\, and its product with the complex plane X x
C. \nA Lagrangian cobordism is a Lagrangian submanifold in X x C whose no
ncompact \nends suitably limit to Lagrangian submanifolds of X. In this ta
lk\, we'll discuss \nhow every Lagrangian submanifold can be decomposed in
to some simple pieces - \nsurgery traces and suspensions of exact homotopy
. Furthermore\, we'll speculate \nabout the connection between these decom
positions and the work of Biran and Cornea \nrelating Lagrangian cobordism
s to equivalences of Lagrangian Floer cohomology.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Itamar Rosenfeld Rauch (Technion\, Haifa)
DTSTART:20210609T111000Z
DTEND:20210609T123000Z
DTSTAMP:20260404T094529Z
UID:GDS/36
DESCRIPTION:Title: On the Hofer Girth of the Sphere of Great Circles\nby Itamar Rosen
feld Rauch (Technion\, Haifa) as part of Geometry and Dynamics seminar\n\n
\nAbstract\nAn equator of $S^2$ is an embedded circle that divides the sph
ere into two \nequal area discs. Chekanov introduced a distance function o
n the space of \nequators\, induced by the Hofer norm. We define the Hofer
girth of this \nspace\, roughly speaking\, as the smallest diameter of a
non-contractible \nsphere in this space\, as inspired by the classic metri
c invariant of systoles. \nA somewhat natural embedding of $S^2$ in the sp
ace of equators sends each \npoint to the great circle perpendicular to it
\; this embedding is called the \nsphere of great circles.\nIn this talk w
e will discuss a few properties of Hofer girth\, and show that \nthe diame
ter of the sphere of great circles is not optimal\, by constructing \na st
rictly better candidate.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marcelo R.R. Alves (University of Antwerp)
DTSTART:20210616T111000Z
DTEND:20210616T123000Z
DTSTAMP:20260404T094529Z
UID:GDS/37
DESCRIPTION:Title: Entropy collapse versus entropy rigidity for Reeb and Finsler flows\nby Marcelo R.R. Alves (University of Antwerp) as part of Geometry and D
ynamics seminar\n\n\nAbstract\nThe topological entropy of a flow on a comp
act manifold is a measure \nof complexity related to many other notions of
growth. By celebrated \nworks of Katok and Besson-Courtois-Gallot\, the t
opological entropy \nof geodesic flows of Riemannian metrics with a fixed
volume on a \nmanifold M that carries a metric of negative curvature is un
iformly \nbounded from below by a positive constant depending only on M. W
e show \nthat this result persists for all (possibly irreversible) Finsler
\nflows\, but that on every closed contact manifold there exists a Reeb \
nflow of fixed volume and arbitrarily small entropy. This is joint work \n
with Alberto Abbondandolo\, Murat Saglam and Felix Schlenk.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Tsodikovich (Tel Aviv University)
DTSTART:20211027T111000Z
DTEND:20211027T123000Z
DTSTAMP:20260404T094529Z
UID:GDS/38
DESCRIPTION:Title: Billiard Tables with rotational symmetry\nby Daniel Tsodikovich (T
el Aviv University) as part of Geometry and Dynamics seminar\n\n\nAbstract
\nConsider the following simple geometric fact: the only centrally symmetr
ic \nconvex curve of constant width is a circle. The condition of having c
onstant \nwidth is equivalent for the (Birkhoff) billiard map to have a 1-
parameter \nfamily of two periodic orbits. We generalize this statement to
curves that \nare invariant under a rotation by angle $\\frac{2\\pi}{k}$\
, for which the \nbilliard map has a 1-parameter family of k-periodic orb
its. We will also \nconsider a similar setting for other billiard systems:
outer billiards\, \nsymplectic billiards\, and (a special case of) Minkow
ski billiards. \nJoint work with Misha Bialy.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Egor Shelukhin (University of Montreal)
DTSTART:20211103T141000Z
DTEND:20211103T153000Z
DTSTAMP:20260404T094529Z
UID:GDS/39
DESCRIPTION:Title: Hamiltonian no-torsion\nby Egor Shelukhin (University of Montreal)
as part of Geometry and Dynamics seminar\n\n\nAbstract\nWe generalize in
several ways Polterovich's well-known theorem that the \nHamiltonian group
of a closed symplectically aspherical manifold admits \nno non-trivial el
ements of finite order. We prove an analogous statement \nfor Calabi-Yau a
nd negatively monotone manifolds. For positively monotone \nmanifolds we p
rove that non-trivial torsion implies geometric uniruledness \nof the mani
fold\, answering a question of McDuff-Salamon. Moreover\, in this \ncase t
he following symplectic Newman theorem holds: a small Hofer-ball \naround
the identity contains no finite subgroup. This is joint work with \nMarcel
o Atallah.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Umut Varolgunes (Stanford University\, University of Edinburgh)
DTSTART:20211110T121000Z
DTEND:20211110T133000Z
DTSTAMP:20260404T094529Z
UID:GDS/40
DESCRIPTION:Title: Trying to quantify Gromov's non-squeezing theorem\nby Umut Varolgu
nes (Stanford University\, University of Edinburgh) as part of Geometry an
d Dynamics seminar\n\n\nAbstract\nGromov's celebrated result says (colloqu
ially) that one cannot symplectically \nembed a ball of radius 1.1 into a
cylinder of radius 1. I will show that in \n4d if one removes from this ba
ll a Lagrangian plane passing through the \norigin\, then such an embeddin
g becomes possible. I will also show that this \ngives the smallest Minkow
ski dimension of a closed subset with this property. \nI will end with man
y questions. This is based on joint work with K. Sackel\, \nA. Song and J.
Zhu.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pazit Haim Kislev (Tel Aviv University)
DTSTART:20211117T121000Z
DTEND:20211117T133000Z
DTSTAMP:20260404T094529Z
UID:GDS/41
DESCRIPTION:Title: Symplectic capacities of p-products\nby Pazit Haim Kislev (Tel Avi
v University) as part of Geometry and Dynamics seminar\n\n\nAbstract\nIn t
his talk we discuss symplectic capacities of convex domains and their \nbe
havior with respect to symplectic p-products. One application\, by using \
na "tensor power trick"\, is to show that it is enough to prove Viterbo's
\nvolume-capacity conjecture in the asymptotic regime when the dimension i
s \nsent to infinity. In addition\, we introduce a conjecture about higher
order \ncapacities of p-products and show that if it holds then there are
no \nnon-trivial p-decompositions of the symplectic ball.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gerhard Knieper (Ruhr University Bochum)
DTSTART:20211124T121000Z
DTEND:20211124T133000Z
DTSTAMP:20260404T094529Z
UID:GDS/42
DESCRIPTION:Title: Growth rate of closed geodesics on surfaces without conjugate points\nby Gerhard Knieper (Ruhr University Bochum) as part of Geometry and Dy
namics seminar\n\n\nAbstract\nLet (M\,g) be a closed Riemannian surface of
of genus at least 2 and no \nconjugate points. By the uniformization theo
rem such a surface admits\na metric of negative curvature and therefore th
e topological entropy h \nof the geodesic flow is positive. Denote by P(t)
the number of free \nhomotopy classes containing a closed geodesic of p
eriod $\\le t $. We \nwill show: P(t) is asymptotically equivalent to e^(h
t)/(ht) =F(t)\, i.e. \nthe ratio of P and F converges to 1 as t tends to
infinity. \nAn important ingredient in the proof is a mixing flow invarian
t measure \ngiven by the unique measure of maximal entropy. Under suitable
hyperbolicity \nassumptions this result carries over to closed Riemannian
manifolds without \nconjugate and higher dimension.\n\nFor closed manifol
ds of negative curvature the above estimate is well known \nand has been o
riginally obtained by Margulis. In a recent preprint\nthe estimate has bee
n also obtained by Ricks for certain closed manifolds \n(rank 1 mflds) of
non-positive curvature. This is a joint work with Vaughn \nClimenhaga and
Khadim War.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sara Tukachinsky (Tel Aviv University)
DTSTART:20211129T131000Z
DTEND:20211129T143000Z
DTSTAMP:20260404T094529Z
UID:GDS/43
DESCRIPTION:Title: Bounding chains as a tool in open Gromov-Witten theory\nby Sara Tu
kachinsky (Tel Aviv University) as part of Geometry and Dynamics seminar\n
\n\nAbstract\nModuli spaces of J-holomorphic disks have boundary. This int
erferes with \ndesirable structures\, such as Lagrangian Floer theory or o
pen Gromov-Witten \ninvariants. One tool for balancing out boundary contri
butions is a bounding \nchain. In this talk I will give some background on
the problem\, then discuss \nin detail what bounding chains are\, how the
y can be constructed\, and how \nthey are used to define invariants. \nThe
work of several people will be mentioned\, among them a joint work \nwith
J. Solomon.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louis Ioos (Max Planck Institute)
DTSTART:20211208T121000Z
DTEND:20211208T133000Z
DTSTAMP:20260404T094529Z
UID:GDS/44
DESCRIPTION:Title: Quantization in stages and canonical metrics\nby Louis Ioos (Max P
lanck Institute) as part of Geometry and Dynamics seminar\n\n\nAbstract\nI
n this talk\, I will introduce the notion of quantization in stages\, whic
h \nlies at the basis of fundamental physical set-ups such as the Stern-Ge
rlach \nexperiment\, and explain how it can be realized over compact sympl
ectic phase \nspaces via the use of Berezin-Toeplitz quantization of vecto
r bundles. In \nparticular\, I will introduce and show how to compute the
associated quantum \nnoise. I will then describe an application to Hermite
-Einstein metrics on \nstable vector bundles over a projective manifold\,
and if time permits\, I will \nshow how a refinement of these results in t
he case of the trivial line bundle \ncan be applied to Kähler metrics of
constant scalar curvature.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Philippe Charron (Technion)
DTSTART:20211215T121000Z
DTEND:20211215T133000Z
DTSTAMP:20260404T094529Z
UID:GDS/45
DESCRIPTION:Title: Pleijel's theorem for Schrödinger operators\nby Philippe Charron
(Technion) as part of Geometry and Dynamics seminar\n\n\nAbstract\nWe will
discuss some recent results regarding the number of nodal domains \nof La
place and Schrödinger operators. Improving on Courant's seminal work\, \n
Pleijel's original proof in 1956 was only for domains in R^2 with Dirichle
t \nboundary conditions\, but it was later generalized to manifolds (Peetr
e and \nBérard-Meyer) with Dirichlet boundary conditions\, then to planar
domains with \nNeumann Boundary conditions (Polterovich\, Léna)\, but al
so to the quantum \nharmonic oscillator (C.) and to Schrödinger operators
with radial potentials \n(C. - Helffer - Hoffmann-Ostenhof). In this rece
nt work with Corentin Léna\, \nwe proved Pleijel's asymptotic upper bound
for a much larger class of \nSchrödinger operators which are not necessa
rily radial. In this talk\, I will \nexplain the problems that arise from
studying Schrödinger operators as well \nas the successive improvements i
n the methods that led to the current results.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simion Filip (University of Chicago)
DTSTART:20211222T121000Z
DTEND:20211222T133000Z
DTSTAMP:20260404T094529Z
UID:GDS/46
DESCRIPTION:Title: Anosov representations\, Hodge theory\, and Lyapunov exponents\nby
Simion Filip (University of Chicago) as part of Geometry and Dynamics sem
inar\n\n\nAbstract\nDiscrete subgroups of semisimple Lie groups arise in a
variety of contexts\, \nsometimes "in nature" as monodromy groups of fami
lies of algebraic manifolds\, \nand other times in relation to geometric s
tructures and associated dynamical \nsystems. I will discuss a class of su
ch discrete subgroups that arise from \ncertain variations of Hodge struct
ure and lead to Anosov representations\, thus \nrelating algebraic and dyn
amical situations. Among many consequences of these \nrelations\, I will e
xplain Torelli theorems for certain families of Calabi-Yau \nmanifolds (in
cluding the mirror quintic)\, uniformization results for domains \nof disc
ontinuity of the associated discrete groups\, and also a proof of a \nconj
ecture of Eskin\, Kontsevich\, Moller\, and Zorich on Lyapunov exponents.
\nThe discrete groups of interest live inside the real linear symplectic g
roup\, \nand the domains of discontinuity are inside Lagrangian Grassmania
ns and other \nassociated flag manifolds. The necessary context and backgr
ound will be explained.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Uljarević (University of Belgrade)
DTSTART:20220105T121000Z
DTEND:20220105T133000Z
DTSTAMP:20260404T094529Z
UID:GDS/47
DESCRIPTION:Title: Contact non-squeezing via selective symplectic homology\nby Igor U
ljarević (University of Belgrade) as part of Geometry and Dynamics semina
r\n\n\nAbstract\nIn this talk\, I will introduce a new version of symplect
ic homology\, \ncalled "selective symplectic homology"\, that is associate
d to a\nLiouville domain and an open subset of its boundary. The selective
\nsymplectic homology is obtained as the direct limit of Floer homology\ng
roups for Hamiltonians whose slopes tend to infinity on the open subset\nb
ut remain close to 0 and positive on the rest of the boundary.\n\nI will s
how how selective symplectic homology can be used to prove\ncontact non-sq
ueezing phenomena. One such phenomenon concerns homotopy\nspheres that can
be filled by a Weinstein domain with infinite\ndimensional symplectic hom
ology: there exists a (smoothly) embedded closed\nball in such a sphere th
at cannot be contactly squeezed into every\nnon-empty open subset. As a co
nsequence\, there exists a contact structure\non the standard smooth spher
e (in certain dimensions) that is homotopic to\nthe standard contact struc
ture but which exhibits\nnon-trivial contact non-squeezing.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joé Brendel (University of Neuchâtel)
DTSTART:20220302T121000Z
DTEND:20220302T133000Z
DTSTAMP:20260404T094529Z
UID:GDS/48
DESCRIPTION:Title: Squeezing the symplectic ball (up to a subset)\nby Joé Brendel (U
niversity of Neuchâtel) as part of Geometry and Dynamics seminar\n\n\nAbs
tract\nIn a recent preprint\, Sackel-Song-Varolgunes-Zhu investigate quant
itative \nquestions surrounding Gromov's non-squeezing theorem. In particu
lar\, they \nshow that if one can embed the four-ball into a cylinder of s
maller capacity \nafter the removal of a subset\, then this subset has Min
kowski dimension at \nleast two. Furthermore\, they give an explicit examp
le of such a "squeezing \nup to a subset" where the subset they remove has
dimension two and allows \nsqueezing by a factor of two (in terms of capa
cities). In this talk\, we will \ndiscuss certain squeezings by a factor o
f up to three. The construction is \ninspired by degenerations of the comp
lex projective plane and almost toric \nfibrations. If time permits\, we w
ill give a construction by hand and discuss \nhow this leads to a differen
t viewpoint on almost toric fibrations and \npotential squeezings in highe
r dimensions. This is partially based on work \nthat will appear as an app
endix of the SSVZ paper.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jake Solomon (Hebrew University of Jerusalem)
DTSTART:20220309T121000Z
DTEND:20220309T133000Z
DTSTAMP:20260404T094529Z
UID:GDS/49
DESCRIPTION:Title: The cylindrical transform\nby Jake Solomon (Hebrew University of J
erusalem) as part of Geometry and Dynamics seminar\n\n\nAbstract\nA Lagran
gian submanifold of a Calabi-Yau manifold is called positive if the \nrest
riction to it of the real part of the holomorphic volume form is positive.
\nThe space of positive Lagrangians admits a Riemannian metric of non-pos
itive \ncurvature. Understanding the geodesics of the space of positive La
grangian \nsubmanifolds would shed light on questions ranging from the uni
queness and \nexistence of volume minimizing Lagrangian submanifolds to Ar
nold's nearby \nLagrangian conjecture. The geodesic equation is a non-line
ar degenerate elliptic \nPDE. I will describe work with A. Yuval on the cy
lindrical transform\, which \nconverts the geodesic equation to a family o
f non-degenerate elliptic boundary \nvalue problems. As a result\, we obta
in examples of geodesics in arbitrary \ndimension that are not invariant u
nder any isometries. The talk will be aimed \nat a broad audience.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dustin Connery-Grigg (University of Montreal)
DTSTART:20220316T141000Z
DTEND:20220316T153000Z
DTSTAMP:20260404T094529Z
UID:GDS/50
DESCRIPTION:by Dustin Connery-Grigg (University of Montreal) as part of Ge
ometry and Dynamics seminar\n\n\nAbstract\nIn general\, it is difficult to
relate the structure of the Hamiltonian Floer \ncomplex of a generic pair
(H\,J) to the dynamical behaviour of the Hamiltonian \nsystem generated b
y H. However\, it turns out that in dimension 2\, topological \nobstructio
ns coming from the braid-theoretic structure of the periodic orbits \nallo
w us to make significant inroads into understanding the geometric and dyna
mical \ncontent of Hamiltonian Floer theory. Some highlights include a top
ological \ncharacterization of those Floer chains which represent the fund
amental class \n(and which moreover lie in the image of some chain-level P
SS map)\, as well as \nan interpretation of the structure of Floer chain c
omplexes in homologically \nnon-trivial degrees in terms of particularly w
ell-behaved singular foliations \nwhich may be thought of as generalizatio
ns of Poincare sections. In this talk\, \nI will present the main ideas an
d techniques which go into establishing such \nresults and attempt to sket
ch some of the main lines of argument involved in \ntheir proof.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pranav Chakravarthy (Hebrew University of Jerusalem)
DTSTART:20220323T121000Z
DTEND:20220323T133000Z
DTSTAMP:20260404T094529Z
UID:GDS/51
DESCRIPTION:Title: Homotopy type of equivariant symplectomorphisms of rational ruled surf
aces\nby Pranav Chakravarthy (Hebrew University of Jerusalem) as part
of Geometry and Dynamics seminar\n\n\nAbstract\nIn this talk\, we present
results on the homotopy type of the group of \nequivariant symplectomorphi
sms of $S^2 \\times S^2$ and $\\mathbb{C}P^2$ blown \nup once\, under the
presence of Hamiltonian group actions of either $S^1$ or \nfinite cyclic
groups. For Hamiltonian circle actions\, we prove that the \ncentralizers
are homotopy equivalent to either a torus or to the homotopy \npushout of
two tori depending on whether the circle action extends to a single \ntor
ic action or to exactly two non-equivalent toric actions. We can show that
\nthe same holds for the centralizers of most finite cyclic groups in the
\nHamiltonian group. Our results rely on J-holomorphic techniques\, on De
lzant's \nclassification of toric actions\, on Karshon's classification of
Hamiltonian \ncircle actions on 4-manifolds\, and on the Chen-Wilczy\\'ns
ki smooth \nclassification of $\\mathbb{Z}_n$-actions on Hirzebruch surfac
es.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maksim Stokic (Tel Aviv University)
DTSTART:20220330T111000Z
DTEND:20220330T123000Z
DTSTAMP:20260404T094529Z
UID:GDS/52
DESCRIPTION:Title: $C^0$ contact geometry of isotropic submanifolds\nby Maksim Stokic
(Tel Aviv University) as part of Geometry and Dynamics seminar\n\n\nAbstr
act\nThe celebrated Eliashberg-Gromov rigidity theorem states that a diffe
omorphism \nwhich is a $C^0$-limit of symplectomorphisms is itself symplec
tic. Contact \nversion of this rigidity theorem holds true as well. Motiva
ted by this\, contact \nhomeomorphisms are defined as $C^0$-limits of cont
actomorphisms. Isotropic \nsubmanifolds are a particularly interesting cla
ss of submanifolds\, and in this \ntalk we will try to answer whether or n
ot isotropic property is preserved by \ncontact homeomorphisms. Legendrian
submanifolds are isotropic submanifolds of \nmaximal dimension and we exp
ect that the rigidity holds in this case. We give \na new proof of the rig
idity in dimension 3\, and provide some type of rigidity \nin higher dimen
sions. On the other hand\, we show that the subcritical isotropic \ncurves
are flexible\, and we prove quantitative $h$-principle for subcritical \n
isotropic embeddings which is our main tool for proving the flexibility re
sult.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sheng-Fu Chiu (Institute of Mathematics\, Academia Sinica\, Taiwan
)
DTSTART:20220406T111000Z
DTEND:20220406T123000Z
DTSTAMP:20260404T094529Z
UID:GDS/53
DESCRIPTION:Title: From Energy-Time Uncertainty to Symplectic Displacement Energy\nby
Sheng-Fu Chiu (Institute of Mathematics\, Academia Sinica\, Taiwan) as pa
rt of Geometry and Dynamics seminar\n\n\nAbstract\nHeisenberg's Uncertaint
y Principle is one of the most celebrated features of \nquantum mechanics\
, which states that one cannot simultaneously obtain the \nprecise measure
ments of two conjugated physical quantities such as the pair \nof position
and momentum or the pair of electric potential and charge density. \nAmon
g the different formulations of this fundamental quantum property\, the \n
uncertainty between energy and time has a special place. This is because t
he \ntime is rather a variable parametrizing the system evolution than a p
hysical \nquantity waiting for determination. Physicists working on the fo
undation of \nquantum theory have understood this energy-time relation by
a universal bound \nof how fast any quantum system with given energy can e
volve from one state to \nanother in a distinguishable (orthogonal) way. R
ecently\, there have been many \narguing that this bound is not a pure qua
ntum phenomenon but a general \ndynamical property of Hilbert space. In th
is talk\, in contrast to the usual \nHilbert space formalism\, we will pro
vide a homological viewpoint of this \nevolutional speed limit based on a
persistence-like distance of the derived \ncategory of sheaves : during a
time period what is the minimal energy needed \nfor a system to evolve fro
m one sheaf to a status that is distinguishable from \na given subcategory
? As an application\, we will also discuss its geometric \nincarnation in
the dynamics of classical mechanics\, namely the notion of \nsymplectic di
splacement. We will see how this categorical energy manages to \ncharacter
ize the symplectic energy for disjointing a Lagrangian from an open set.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Brandenbursky (Ben-Gurion University)
DTSTART:20220427T111000Z
DTEND:20220427T120000Z
DTSTAMP:20260404T094529Z
UID:GDS/54
DESCRIPTION:Title: C^0-gap between entropy-zero Hamiltonians and autonomous diffeomorphis
ms of surfaces\nby Michael Brandenbursky (Ben-Gurion University) as pa
rt of Geometry and Dynamics seminar\n\n\nAbstract\nLet Σ be a surface equ
ipped with an area form. There is a long standing open \nquestion by Katok
\, which\, in particular\, asks whether every entropy-zero \nHamiltonian d
iffeomorphism of a surface lies in the C^0-closure of the set \nof integra
ble diffeomorphisms. A slightly weaker version of this question \nasks: ``
Does every entropy-zero Hamiltonian diffeomorphism of a surface lie \nin t
he C^0-closure of the set of autonomous diffeomorphisms?'' In this talk \n
I will answer in negative the later question. In particular\, I will show
that \non a surface Σ the set of autonomous Hamiltonian diffeomorphisms i
s not \nC^0-dense in the set of entropy-zero Hamiltonians. Explicitly cons
tructed \nexamples of such Hamiltonians cannot be approximated by autonomo
us \ndiffeomorphisms. (Joint with M. Khanevsky).\n
LOCATION:https://stable.researchseminars.org/talk/GDS/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Umut Varolgunes (Bogazici University)
DTSTART:20220427T121000Z
DTEND:20220427T130000Z
DTSTAMP:20260404T094529Z
UID:GDS/55
DESCRIPTION:Title: Computations in relative symplectic cohomology using local to global m
ethods\nby Umut Varolgunes (Bogazici University) as part of Geometry a
nd Dynamics seminar\n\n\nAbstract\nConsider a complete Lagrangian torus fi
bration p(n) from a symplectic manifold \nto the plane with at most one si
ngular fiber which is a two torus pinched at \nn-meridians. Relative sympl
ectic cohomology in degree 0 defines a sheaf of \nalgebras in the base wit
h respect to an appropriate G-topology and grading \ndatum. I will explain
how one can compute this sheaf for all p(n) using \ngeneral properties an
d explicit computations for p(0). This is a joint work \nwith Yoel Groman.
\n
LOCATION:https://stable.researchseminars.org/talk/GDS/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Egor Shelukhin (University of Montreal)
DTSTART:20220501T110000Z
DTEND:20220501T115000Z
DTSTAMP:20260404T094529Z
UID:GDS/56
DESCRIPTION:Title: The transcendental Bézout problem revisited\nby Egor Shelukhin (U
niversity of Montreal) as part of Geometry and Dynamics seminar\n\n\nAbstr
act\nBézout's classical theorem states that n complex polynomials of degr
ee k on C^n \nhave at most k^n isolated common zeros. The logarithm of the
maximal function \nof an entire function on C\, instead of the degree\, c
ontrols the number of zeros \nin a ball of radius r. The transcendental B
ézout problem seeks to extend this \nestimate to entire self-mappings f o
f C^n via the n-th power of the logarithm \nof the maximal function. A cel
ebrated counterexample of Cornalba-Shiffman shows \nthat this is dramatica
lly false for n>1. However\, it is true on average\, under \nlower bounds
on the Jacobian\, or in a weaker form for small constant perturbations \no
f f. We explain how topological considerations of persistent homology and
\nMorse theory shed new light on this question proving the expected bound
for a \nrobust count of zeros. This is part of a larger joint project with
Buhovsky\, \nPayette\, Polterovich\, Polterovich\, and Stojisavljevic.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hyunmoon Kim (Seoul National University)
DTSTART:20220511T111000Z
DTEND:20220511T123000Z
DTSTAMP:20260404T094529Z
UID:GDS/57
DESCRIPTION:Title: Complex Lagrangian subspaces and representations of the canonical comm
utation relations\nby Hyunmoon Kim (Seoul National University) as part
of Geometry and Dynamics seminar\n\n\nAbstract\nComplex Lagrangian subspa
ces were introduced as polarizations on symplectic \nmanifolds in geometri
c quantization. We will look at their role in the linear \ngeometry more c
arefully. A transverse pair of complex Lagrangian subspaces \nparametrizes
representations of the canonical commutation relations and this \nbrings
together some different perspectives from which the representations \nwere
studied. I will suggest how this result can be interpreted using concepts
\nfrom geometry and very little concepts from physics.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ofir Karin (Tel Aviv University)
DTSTART:20220518T111000Z
DTEND:20220518T120000Z
DTSTAMP:20260404T094529Z
UID:GDS/58
DESCRIPTION:Title: Approximation of Generating Function Barcode for Hamiltonian Diffeomor
phisms\nby Ofir Karin (Tel Aviv University) as part of Geometry and Dy
namics seminar\n\n\nAbstract\nPersistence modules and barcodes are used in
symplectic topology to define \nnew invariants of Hamiltonian diffeomorph
isms\, however methods that explicitly \ncalculate these barcodes are ofte
n unclear. In this talk I will explain the \nnecessary background and defi
ne one such invariant called the GF-barcode of \ncompactly supported Hamil
tonian diffeomorphisms of $ \\mathbb{R}^{2n} $ by \napplying Morse theory
to generating functions quadratic at infinity associated \nto such Hamilto
nian diffeomorphisms and provide an algorithm (i.e a finite \nsequence of
explicit calculation steps) that approximates it along with a \nfew comput
ation examples. Joint work with Pazit Haim-Kislev.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexey Balitskiy (IAS Princeton\, and Institute for Information Tr
ansmission Problems RAS)
DTSTART:20220518T121000Z
DTEND:20220518T130000Z
DTSTAMP:20260404T094529Z
UID:GDS/59
DESCRIPTION:Title: Systolic freedom and rigidity modulo 2\nby Alexey Balitskiy (IAS P
rinceton\, and Institute for Information Transmission Problems RAS) as par
t of Geometry and Dynamics seminar\n\n\nAbstract\nThe $k$-dimensional syst
ole of a closed Riemannian $n$-dimensional manifold $M$ \nis the infimal $
k$-volume of a non-trivial $k$-cycle (with some coefficients). \nIn '90s\,
Gromov asked if the product of the $k$-systole and the $(n-k)$-systole \n
is bounded from above by the volume of $M$ (up to a dimensional factor)\;
this \nwould manifest the \\emph{systolic rigidity}. Freedman exhibited th
e first \nexamples with $k=1$ and mod 2 coefficients where this fails\; th
is manifests \nthe \\emph{systolic freedom}. In a joint work in progress w
ith Hannah Alpert \nand Larry Guth\, we show that Freedman's examples are
almost as "free" as \npossible\, and the systolic rigidity almost holds\,
with $k=1$ and mod 2 \ncoefficients. Namely\, on a manifold of bounded loc
al geometry\, \n$\\mbox{systole}_1(M) \\cdot \\mbox{systole}_{n-1}(M) \\le
c_\\epsilon \\mbox{volume}(M)^{1+\\epsilon}$\, \nas long as the left-hand
side is finite ($H_1(M\; \\mathbb{Z}/2)$ is non-trivial). \nThe proof\, w
hich I will explain\, is based on the Schoen--Yau--Guth--Papasoglu \nminim
al surface method.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander A. Trost (Ruhr University Bochum)
DTSTART:20220525T111000Z
DTEND:20220525T123000Z
DTSTAMP:20260404T094529Z
UID:GDS/60
DESCRIPTION:Title: Elementary bounded generation for global function fields and some appl
ications\nby Alexander A. Trost (Ruhr University Bochum) as part of Ge
ometry and Dynamics seminar\n\n\nAbstract\nBounded generation (and element
ary bounded generation) are essentially the \nability to write each elemen
t of a given group as products with factors from \na finite collection of
”simple” subgroups of the group in question and with \na uniform bound
on the number of factors needed. These somewhat technical \nproperties we
re initially introduced in the study of the congruence subgroup \nproperty
of arithmetic groups\, but they traditionally also found applications \ni
n the representation theory of these groups\, their subgroup growth and \n
Kazdhan’s Property (T). Recently however\, there has been renewed intere
st in \nthese properties from the area of geometric group theory as bounde
d elementary \ngeneration appears naturally as a technical assumption in v
arious results \nstudying arithmetic groups ranging from the study of conj
ugation-invariant \nnorms on\, say\, SLn as well as in the study of the fi
rst-order theories of \narithmetic groups. Classical results in this area
were usually concerned with \ngroups arising from number fields though and
somewhat surprisingly there are \nfew such results for groups arising fro
m global function fields. In this talk\, \nI will give a short introductio
n about the history of bounded generation in \ngeneral and then present a
general bounded generation for split Chevalley \ngroups arising from globa
l function fields together with some applications \nif time allows.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthias Meiwes (RWTH Aachen University)
DTSTART:20220601T111000Z
DTEND:20220601T123000Z
DTSTAMP:20260404T094529Z
UID:GDS/61
DESCRIPTION:Title: Entropy\, braids\, and Hofer's metric\nby Matthias Meiwes (RWTH Aa
chen University) as part of Geometry and Dynamics seminar\n\n\nAbstract\nT
opological entropy captures the orbit complexity of a dynamical system wit
h \nthe help of a single non-negative number. Detecting robustness of this
number \nunder perturbation is a way to understand stability features of
a chaotic system.\nIn my talk\, I will address the problem of robustness o
f entropy for Hamiltonian \ndiffeomorphisms in terms of Hofer's metric. Ou
r main focus lies on dimension 2\, \nwhere there is a strong connection be
tween topological entropy and the existence \nof specific braid types of p
eriodic orbits. I explain that the construction of \neggbeater maps of Pol
terovich-Shelukhin and their generalizations by Chor provide \nrobustness
even under large perturbation: the entropy will not drop much when \npertu
rbing the specific diffeomorphism in some ball of large Hofer-radius. \nI
furthermore discuss a result that any braid of non-degenerate one-periodic
\norbits with pairwise homotopic strands persists under generic Hofer-sma
ll \nperturbations\, which yields a local entropy robustness result for su
rfaces.\nThis talk is based on joint works with Arnon Chor\, and Marcelo A
lves.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Miyamoto (University of Toronto)
DTSTART:20220608T111000Z
DTEND:20220608T123000Z
DTSTAMP:20260404T094529Z
UID:GDS/62
DESCRIPTION:Title: Quasifold groupoids and diffeological quasifolds\nby David Miyamot
o (University of Toronto) as part of Geometry and Dynamics seminar\n\n\nAb
stract\nA quasifold is a space that is locally modeled by quotients of R^n
\nby countable group actions. These arise in Elisa Prato's generalization
of \nthe Delzant theorem to irrational polytopes\, and include orbifolds
and \nmanifolds. We approach quasifolds in two ways: by viewing them as di
ffeological \nspaces\, we form the category of diffeological quasifolds\,
and by viewing them \nas Lie groupoids (with bibundles as morphisms)\, we
form the category of \nquasifold groupoids. We show that\, restricting to
effective groupoids\, and \nlocally invertible morphisms\, these two categ
ories are equivalent. In \nparticular\, an effective quasifold groupoid is
determined by its diffeological \norbit space. This is join work with Yae
l Karshon.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cheuk Yu Mak (University of Edinburgh)
DTSTART:20221026T111000Z
DTEND:20221026T123000Z
DTSTAMP:20260404T094529Z
UID:GDS/63
DESCRIPTION:Title: Some cute applications of Lagrangian cobordisms\nby Cheuk Yu Mak (
University of Edinburgh) as part of Geometry and Dynamics seminar\n\n\nAbs
tract\nIn this talk\, we will discuss\, from a quantitative aspect\, the f
ollowing \nsymplectic questions: packing Lagrangian submanifolds\, displac
ing Lagrangian \nsubmanifolds\, and constructing Lagrangian surfaces with
a prescribed genus. \nWe will illustrate some interesting features of thes
e questions using simple \nexamples. The focus will be put on explaining s
ome new ideas from the point \nof view of Lagrangian cobordisms. This is a
joint work with Jeff Hicks.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierre-Alexandre Mailhot (University of Montreal)
DTSTART:20221102T151000Z
DTEND:20221102T163000Z
DTSTAMP:20260404T094529Z
UID:GDS/64
DESCRIPTION:Title: Spectral diameter\, Liouville domains and symplectic cohomology\nb
y Pierre-Alexandre Mailhot (University of Montreal) as part of Geometry an
d Dynamics seminar\n\n\nAbstract\nThe spectral norm provides a lower bound
to the Hofer norm. It is thus \nnatural to ask whether the diameter of th
e spectral norm is finite or not. \nIn the case of closed symplectic manif
olds\, there is no unified answer. \nFor instance\, for a certain class of
symplecticaly aspherical manifolds\, \nwhich contains surfaces\, the spec
tral diameter is infinite. However\, for \nCP^n\, the spectral diameter is
known to be finite. During this talk\, I will \nprove that\, in the case
of Liouville domains\, the spectral diameter is \nfinite if and only if th
e symplectic cohomology of the underlying manifold \nvanishes. With that r
elationship in hand\, we will explore applications to \nsymplecticaly asph
erical symplectic manifolds and give a new proof that the \nspectral diame
ter is infinite on cotangent disk bundles.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Grigory Mikhalkin (University of Geneva)
DTSTART:20221109T121000Z
DTEND:20221109T133000Z
DTSTAMP:20260404T094529Z
UID:GDS/65
DESCRIPTION:Title: Toric geometry and tropical trigonometry\nby Grigory Mikhalkin (Un
iversity of Geneva) as part of Geometry and Dynamics seminar\n\n\nAbstract
\nToric varieties were constructed as algebraic varieties about 50 years a
go\, \nand also as symplectic varieties about 40 years ago. The two constr
uctions \nare dual to each other\, but are based on the same geometry in R
^n. Symmetries \nin this geometry are linear transformations given by inve
rtible n-by-n \nmatrices with integer coefficients\, as well as all transl
ations. This makes \nthe notion of a tangent integer vector as well as a n
otion of tropical curve \nwell-defined. The talk will review basic constru
ctions with a focus on \ntropical triangles that underlie some recent prog
ress in symplectic embedding \nproblems.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jinxin Xue (Tsinghua University)
DTSTART:20221116T121000Z
DTEND:20221116T133000Z
DTSTAMP:20260404T094529Z
UID:GDS/66
DESCRIPTION:Title: Dynamics of composite symplectic Dehn twists\nby Jinxin Xue (Tsing
hua University) as part of Geometry and Dynamics seminar\n\n\nAbstract\nIt
is classically known in Nielson-Thurston theory that the mapping class \n
group of a hyperbolic surface is generated by Dehn twists and most element
s \nare pseudo Anosov. Pseudo Anosov elements are interesting dynamical ob
jects. \nThey are featured by positive topological entropy and two invaria
nt singular \nfoliations expanded or contracted by the dynamics. We explor
e a generalization \nof these ideas to symplectic mapping class groups. Wi
th the symplectic Dehn \ntwists along Lagrangian spheres introduced by Arn
old and Seidel\, we show in \nvarious settings that the compositions of s
uch twists has features of pseudo \nAnosov elements\, such as positive top
ological entropy\, invariant stable and \nunstable laminitions\, exponenti
al growth of Floer homology group\, etc. This \nis a joint work with Wenmi
n Gong and Zhijing Wang.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marcelo S. Atallah (University of Montreal)
DTSTART:20221123T151000Z
DTEND:20221123T163000Z
DTSTAMP:20260404T094529Z
UID:GDS/67
DESCRIPTION:Title: Fixed points of small Hamiltonian diffeomorphisms and the Flux conject
ures\nby Marcelo S. Atallah (University of Montreal) as part of Geomet
ry and Dynamics seminar\n\n\nAbstract\nInspired by the work of Lalonde-McD
uff-Polterovich\, we describe how the C^0 \nand C^1 flux conjectures relat
e to new instances of the strong Arnol’d \nconjecture and make new progr
ess on the C^0 flux conjecture. This is joint \nwork in progress with Egor
Shelukhin.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joé Brendel (Tel Aviv University)
DTSTART:20221130T121000Z
DTEND:20221130T133000Z
DTSTAMP:20260404T094529Z
UID:GDS/68
DESCRIPTION:Title: Pinwheels as Lagrangian barriers\nby Joé Brendel (Tel Aviv Univer
sity) as part of Geometry and Dynamics seminar\n\n\nAbstract\nPinwheels ar
e certain singular Lagrangians in four-dimensional \nsymplectic manifolds.
In this talk we focus on the case of the complex \nprojective plane\, whe
re pinwheels arise naturally as visible Lagrangians \nin its almost toric
fibrations or\, alternatively\, as vanishing cycles of \nits degenerations
. Pinwheels have been shown to have interesting \nrigidity properties by E
vans--Smith. The goal of this talk is to show \nthat Lagrangian pinwheels
are Lagrangian barriers in the sense of Biran\, \nmeaning that their compl
ement has strictly smaller Gromov width than the \nambient space. Furtherm
ore\, we will discuss a connection to the Lagrange \nspectrum. This is joi
nt work with Felix Schlenk.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yoel Groman (Hebrew University of Jerusalem)
DTSTART:20221207T121000Z
DTEND:20221207T133000Z
DTSTAMP:20260404T094529Z
UID:GDS/69
DESCRIPTION:Title: Closed string mirrors of symplectic cluster manifolds\nby Yoel Gro
man (Hebrew University of Jerusalem) as part of Geometry and Dynamics semi
nar\n\n\nAbstract\nConsider a symplectic Calabi Yau manifold equipped with
a Maslow 0 Lagrangian \ntorus fibration with singularities. According to
modern interpretations of \nthe SYZ conjecture\, there should be an associ
ated analytic mirror variety \nwith a non Archimedean torus fibration ove
r the same base. I will suggest a \ngeneral construction called the closed
string mirror which is based on \nrelative symplectic cohomologies of the
fibers. A priori the closed string \nmirror is only a set with a map to t
he base\, but conjecturally under some \ngeneral hypotheses it is in fact
an analytic variety with its non Archimedean \ntorus fibration. I will dis
cuss joint work with Umut Varolgunes where we prove \nthis in the case of
four dimensional symplectic cluster manifolds.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mira Shamis (Queen Mary University of London)
DTSTART:20221214T121000Z
DTEND:20221214T133000Z
DTSTAMP:20260404T094529Z
UID:GDS/70
DESCRIPTION:Title: On the abominable properties of the Almost Mathieu operator with Liouv
ille frequencies\nby Mira Shamis (Queen Mary University of London) as
part of Geometry and Dynamics seminar\n\n\nAbstract\nWe show that\, for su
fficiently well approximable frequencies\, several\nspectral characteristi
cs of the Almost Mathieu operator can be as poor\nas at all possible in th
e class of all discrete Schroedinger\noperators. For example\, the modulus
of continuity of the integrated\ndensity of states may be no better than
logarithmic. Other\ncharacteristics to be discussed are homogeneity\, the
Parreau-Widom\nproperty\, and (for the critical AMO) the Hausdorff content
of the\nspectrum. Based on joint work with A. Avila\, Y. Last\, and Q. Zh
ou.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maksim Stokic (Tel Aviv University)
DTSTART:20221221T121000Z
DTEND:20221221T133000Z
DTSTAMP:20260404T094529Z
UID:GDS/71
DESCRIPTION:Title: Flexibility of the adjoint action of the group of Hamiltonian diffeomo
rphisms\nby Maksim Stokic (Tel Aviv University) as part of Geometry an
d Dynamics seminar\n\n\nAbstract\nThe space of Hamiltonian diffeomorphisms
has a structure of an infinite \ndimensional Frechet Lie group\, with Lie
algebra isomorphic to the space \nof normalized functions and adjoint act
ion given by pull-backs. We show \nthat this action is flexible: for a non
-zero normalized function $f$\, \nany other normalized function can be wri
tten as a sum of differences of \nelements in the orbit of $f$ generated b
y the adjoint action. Additionally\, \nthe number of elements in this sum
is dominated from above by the \n$L_{\\infty}$-norm of $f$. This result ca
n be interpreted as an (bounded) \ninfinitesimal version of the Banyaga's
result on simplicity of $Ham(M\,\\omega)$. \nMoreover\, it can be used to
remove the $C^{\\infty}$-continuity condition \nin the Buhovsky-Ostrover t
heorem on the uniqueness of Hofer's metric. \nThis is joint work with Lev
Buhovsky.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Albert Fathi (Georgia Tech)
DTSTART:20221228T121000Z
DTEND:20221228T133000Z
DTSTAMP:20260404T094529Z
UID:GDS/72
DESCRIPTION:Title: Smooth Lyapunov functions on closed subsets and isolating neighbourhoo
ds\nby Albert Fathi (Georgia Tech) as part of Geometry and Dynamics se
minar\n\n\nAbstract\nWe will discuss unified and simplified proofs of some
previously known \ntheorems relating dynamics and Lyapunov functions. In
particular\, we \nwill give a proof of the existence of isolating blocks f
or isolated \ninvariant sets.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shira Tanny (IAS Princeton)
DTSTART:20230104T132000Z
DTEND:20230104T143000Z
DTSTAMP:20260404T094529Z
UID:GDS/73
DESCRIPTION:Title: Closing lemmas in contact dynamics and holomorphic curves\nby Shir
a Tanny (IAS Princeton) as part of Geometry and Dynamics seminar\n\n\nAbst
ract\nGiven a flow on a manifold\, how to perturb it in order to create a
periodic \norbit passing through a given region? While the first results i
n this \ndirection were obtained in the 1960-ies\, various facets of this
question \nremain largely open. I will review recent advances on this prob
lem in the \ncontext of contact flows\, which are closely related to Hamil
tonian flows \nfrom classical mechanics. In particular\, I'll discuss a pr
oof of a \nconjecture of Irie stating that rotations of odd-dimensional el
lipsoids \nadmit a surprisingly large class of perturbations creating peri
odic orbits. \nThe proof involves methods of modern symplectic topology in
cluding \npseudo-holomorphic curves and contact homology. The talk is base
d on a \njoint work with Julian Chaidez\, Ipsita Datta and Rohil Prasad\,
as well \nas a work in progress joint with Julian Chaidez.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Iosif Polterovich (University of Montreal)
DTSTART:20230104T120000Z
DTEND:20230104T131000Z
DTSTAMP:20260404T094529Z
UID:GDS/74
DESCRIPTION:Title: Pólya's eigenvalue conjecture: some recent advances\nby Iosif Pol
terovich (University of Montreal) as part of Geometry and Dynamics seminar
\n\n\nAbstract\nThe celebrated Pólya’s conjecture (1954) in spectral ge
ometry states that \nthe eigenvalue counting functions of the Dirichlet an
d Neumann Laplacian \non a bounded Euclidean domain can be estimated from
above and below\, \nrespectively\, by the leading term of Weyl’s asympto
tics. The conjecture \nis known to be true for domains which tile the Eucl
idean space\, however \nit remains largely open in full generality. In the
talk we will explain \nthe motivation behind this conjecture and discuss
some recent advances\, \nnotably\, the proof of Pólya’s conjecture for
the disk. The talk is based \non a joint work with Nikolay Filonov\, Micha
el Levitin and David Sher.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuhan Sun (Rutgers University)
DTSTART:20230111T151000Z
DTEND:20230111T163000Z
DTSTAMP:20260404T094529Z
UID:GDS/75
DESCRIPTION:Title: Heavy sets and relative symplectic cohomology\nby Yuhan Sun (Rutge
rs University) as part of Geometry and Dynamics seminar\n\n\nAbstract\nHea
vy sets were introduced by Entov-Polterovich around 2009. They reveal \nsu
prising rigidity of certain compact subsets of a closed symplectic manifol
d\, \nfrom a functional persepective. When a compact subset is a smooth La
grangian \nsubmanifold\, there is a well-established relation between its
heaviness and \nthe non-vanishing of its Lagrangian Floer cohomology. In t
his talk we \ndescribe an equivalence between the heaviness of general com
pact subsets \nand the non-vanishing of another Floer-type invariant\, cal
led the relative \nsymplectic cohomology. If time permits\, we will discus
s applications and \nquestions we learned from this equivalence. Based on
joint work with C.Mak \nand U.Varolgunes.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Entov (Technion)
DTSTART:20230118T121000Z
DTEND:20230118T133000Z
DTSTAMP:20260404T094529Z
UID:GDS/76
DESCRIPTION:Title: Kahler-type embeddings of balls into symplectic manifolds\nby Mich
ael Entov (Technion) as part of Geometry and Dynamics seminar\n\n\nAbstrac
t\nA symplectic embedding of a disjoint union of balls into a symplectic \
nmanifold M is called Kahler-type if it is holomorphic with respect \nto s
ome (not a priori fixed) complex structure on M compatible with \nthe symp
lectic form. Assume that M either of the following: CP^n (with \nthe stand
ard symplectic form)\, an even-dimensional torus or a K3 surface \nequippe
d with an irrational Kahler-type symplectic form. Then: \n\n1. Any two Kah
ler-type embeddings of a disjoint union of balls into M \ncan be mapped in
to each other by a symplectomorphism acting trivially on \nthe homology. I
f the embeddings are holomorphic with respect to complex \nstructures comp
atible with the symplectic form and lying in the same \nconnected componen
t of the space of Kahler-type complex structures on M\, \nthen the symplec
tomorphism can be chosen to be smoothly isotopic to the \nidentity. \n\n2.
Symplectic volume is the only obstruction for the existence of \nKahler-t
ype embeddings of k^n equal balls (for any k) into CP^n and of \nany numbe
r of possibly different balls into a torus or a K3 surface.\n \nThis is a
joint work with M.Verbitsky.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ely Kerman (University of Illinois Urbana-Champaign)
DTSTART:20230315T121000Z
DTEND:20230315T133000Z
DTSTAMP:20260404T094529Z
UID:GDS/77
DESCRIPTION:Title: Mean width\, symplectic capacities and volume\nby Ely Kerman (Univ
ersity of Illinois Urbana-Champaign) as part of Geometry and Dynamics semi
nar\n\n\nAbstract\nIn this talk\, I will discuss an inequality between a s
ymplectic version \nof the mean width of a convex body and its symplectic
capacity. This is \nmotivated by and generalizes an equality established b
y Artstein-Avidan \nand Ostrover. The proof utilizes their symplectic Brun
n-Minkowski \ninequality together with a local version of Viterbo's conjec
ture \nestablished by Abbondandolo and Benedetti. I will also describe sev
eral \nexamples and secondary results that suggest that the difference bet
ween \nthe symplectic mean width and the mean width is deeply related to t
oric \nsymmetry. This is joint work in progress with Jonghyeon Ahn.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pazit Haim-Kislev (Tel Aviv University)
DTSTART:20230329T111000Z
DTEND:20230329T123000Z
DTSTAMP:20260404T094529Z
UID:GDS/78
DESCRIPTION:Title: Symplectic Barriers\nby Pazit Haim-Kislev (Tel Aviv University) as
part of Geometry and Dynamics seminar\n\n\nAbstract\nIn his seminal 2001
paper\, Biran introduced the concept of Lagrangian \nBarriers\, a symplect
ic rigidity phenomenon coming from obligatory \nintersections with Lagrang
ian submanifolds which doesn't come from \nmere topology. Since then sever
al other examples for Lagrangian barriers \nhave been discovered. In this
joint work with Richard Hind and Yaron \nOstrover\, we introduce the first
example (as far as we know) of Symplectic \nBarriers\, a symplectic rigid
ity coming from obligatory intersections of \nsymplectic embeddings with s
ymplectic submanifolds (and in particular \nnot Lagrangian).\n
LOCATION:https://stable.researchseminars.org/talk/GDS/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Viktor L. Ginzburg (University of California\, Santa Cruz)
DTSTART:20230419T111000Z
DTEND:20230419T120000Z
DTSTAMP:20260404T094529Z
UID:GDS/79
DESCRIPTION:Title: Topological Entropy of Reeb Flows\, Barcodes and Floer Theory\nby
Viktor L. Ginzburg (University of California\, Santa Cruz) as part of Geom
etry and Dynamics seminar\n\n\nAbstract\nTopological entropy is one of the
fundamental invariants of a dynamical \nsystem\, measuring its complexity
. In this talk\, we focus on connections \nbetween the topological entropy
of a Hamiltonian dynamical system\, e.g.\, \na Hamiltonian diffeomorphism
or a Reeb or geodesic flow\, and its \nSymplectic/Floer homology. We reca
ll the definition of barcode entropy — \na Floer theoretic counterpart o
f topological entropy — and discuss \npossible ways to extend it to Reeb
flows. The talk is based on joint \nwork with Erman Cineli\, Basak Gurel
and Marco Mazzucchelli.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Başak Z. Gürel (University of Central Florida)
DTSTART:20230419T121000Z
DTEND:20230419T130000Z
DTSTAMP:20260404T094529Z
UID:GDS/80
DESCRIPTION:Title: On the volume of Lagrangian submanifolds\nby Başak Z. Gürel (Uni
versity of Central Florida) as part of Geometry and Dynamics seminar\n\n\n
Abstract\nWe will discuss the continuity property of the surface area of L
agrangian \nsubmanifolds\, or to be more precise its lower semi-continuity
with respect \nto the gamma-norm\, and connections with integral geometry
\, Floer theory \nand barcodes. The talk is based on joint work with Erman
Cineli and \nViktor Ginzburg.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shmuel Weinberger (University of Chicago)
DTSTART:20230503T111000Z
DTEND:20230503T123000Z
DTSTAMP:20260404T094529Z
UID:GDS/81
DESCRIPTION:Title: Torsion\, L^2 cohomology and complexity\nby Shmuel Weinberger (Uni
versity of Chicago) as part of Geometry and Dynamics seminar\n\n\nAbstract
\nAtiyah introduced real valued L^2 betti numbers as a way of\nunderstandi
ng the (usually infinite dimensional) cohomology of\nuniversal covers of f
inite complexes. As far as anyone knows these\nare always integers for to
rsion free fundamental group\, but for groups\nwith torsion very much more
exotic possibilities arise.\n\nWe will use this and an invariant of Cheeg
er and Gromov to see that\nwhenever an oriented smooth manifold of dimensi
on 4k+3 has torsion in\nits fundamental group\, there are many other manif
olds homotopy\nequivalent but not diffeomorphic to it and that in the know
n\nsituations where betti numbers can be irrational there is even an\ninfi
nitely generated group of such! And\, I will also use this\ninvariant to
explain how many simplices (roughly) it takes to build a\nstandard Lens sp
ace. This is based on old work with Stanley Chang\,\nand recent work with
Geunho Lim.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gleb Smirnov (University of Geneva)
DTSTART:20230510T111000Z
DTEND:20230510T120000Z
DTSTAMP:20260404T094529Z
UID:GDS/82
DESCRIPTION:Title: Lagrangian rigidity in K3 surfaces\nby Gleb Smirnov (University of
Geneva) as part of Geometry and Dynamics seminar\n\n\nAbstract\nSheridan-
Smith and Entov-Verbitsky show that every Maslov-zero Lagrangian \ntorus i
n a K3 surface has a nontrivial and primitive homology class. \nIn this ta
lk\, we prove the "nontrivial" part of their theorem with a \ndifferent me
thod and the converse result.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marcelo R. R. Alves (University of Antwerp)
DTSTART:20230510T121000Z
DTEND:20230510T130000Z
DTSTAMP:20260404T094529Z
UID:GDS/83
DESCRIPTION:Title: C^0-stability of topological entropy for 3-dimensional Reeb flows\
nby Marcelo R. R. Alves (University of Antwerp) as part of Geometry and Dy
namics seminar\n\n\nAbstract\nThe C^0-distance on the space of contact for
ms on a contact manifold has \nbeen studied recently by different authors.
It can be thought of as an \nanalogue for Reeb flows of the Hofer metric
on the space of Hamiltonian \ndiffeomorphisms. In this talk\, I will expla
in some recent progress on \nthe stability properties of the topological e
ntropy with respect to this \ndistance. This is joint work with Lucas Dahi
nden\, Matthias Meiwes and \nAbror Pirnapasov.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joé Brendel (Tel Aviv University)
DTSTART:20230517T111000Z
DTEND:20230517T123000Z
DTSTAMP:20260404T094529Z
UID:GDS/84
DESCRIPTION:Title: Lagrangian product tori in $S^2 \\times S^2$\nby Joé Brendel (Tel
Aviv University) as part of Geometry and Dynamics seminar\n\n\nAbstract\n
A Lagrangian product torus in $S^2 \\times S^2$ is a Lagrangian \ntorus ob
tained by taking a product of circles. The main goal of this \ntalk is to
give a symplectic classification of product tori and \nillustrate that int
eresting things can happen in case the symplectic \nform is non-monotone.
We make a detour through toric geometry and \ndiscuss the more general cla
ssification question of toric fibres. If \ntime permits\, we will discuss
related questions and some applications. \nThis is partially based on join
t work with Joontae Kim.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lenya Ryzhik (Stanford University)
DTSTART:20230531T111000Z
DTEND:20230531T123000Z
DTSTAMP:20260404T094529Z
UID:GDS/85
DESCRIPTION:Title: Diffusion of learning models\nby Lenya Ryzhik (Stanford University
) as part of Geometry and Dynamics seminar\n\n\nAbstract\nThe notion of di
ffusion of knowledge goes at least as far back to \nChapter 1 of the "Pick
wick Papers". However\, its mathematical modeling \nin macroeconomics is m
uch more recent. We will discuss some models \nproposed by R. Lucas and B.
Moll about ten years ago.\nVarious versions lead to the mean field games
type PDE and also \ninfinite-dimensional optimal control Hamilton-Jacobi p
roblems. We will \ndiscuss the little mathematical progress but mostly foc
us on the \nmodeling and open questions aspects.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hyunmoon Kim (University of Toronto\, Tel Aviv University)
DTSTART:20230607T111000Z
DTEND:20230607T123000Z
DTSTAMP:20260404T094529Z
UID:GDS/86
DESCRIPTION:Title: The real orbits of complex Lagrangian Grassmannians\nby Hyunmoon K
im (University of Toronto\, Tel Aviv University) as part of Geometry and D
ynamics seminar\n\n\nAbstract\nThe Riemann sphere can be broken up into th
ree orbits of SL(2\, R)\, as \ntwo open hemispheres and a great circle. We
will discuss a generalization \nof this phenomenon in complex Lagrangian
Grassmannians of higher \ndimensions under the action of the real symplect
ic group. We will \ngive formulas for the number of orbits\, incidence rel
ations\, and \ntheir dimensions. We will also show homotopy equivalences b
etween \nthese orbits and some other Grassmannian objects\, and if time pe
rmits\, \na strategy to compute their homology.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lev Birbrair (The Federal University of Ceará and Jagiellonian Un
iversity)
DTSTART:20230614T111000Z
DTEND:20230614T123000Z
DTSTAMP:20260404T094529Z
UID:GDS/87
DESCRIPTION:by Lev Birbrair (The Federal University of Ceará and Jagiello
nian University) as part of Geometry and Dynamics seminar\n\n\nAbstract\nI
am going to describe the first attempt of outer Lipschitz Classification
\nof germs of Semialgebraic Surfaces. We show how the classification \nque
stion can be solved for a special case - the surfaces\, obtained as \na un
ion of two Normally Embedded Hölder triangles.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefan Nemirovski (Steklov Mathematical Institute and Ruhr Univers
ity Bochum)
DTSTART:20230621T111000Z
DTEND:20230621T123000Z
DTSTAMP:20260404T094529Z
UID:GDS/88
DESCRIPTION:Title: Legendrian links and déjà vu moments\nby Stefan Nemirovski (Stek
lov Mathematical Institute and Ruhr University Bochum) as part of Geometry
and Dynamics seminar\n\n\nAbstract\nLegendrian links in the space of null
geodesics of a spacetime\ncan be used to detect "déjà vu moments"\, i.e
. different instances\nat which an observer receives the same light ray. I
n the talk\,\nI'll discuss the relevant class of Legendrian links and some
\nensuing open problems.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/88/
END:VEVENT
END:VCALENDAR